Football journalist Fabrizio Romano shared the manager's words after United's penalty shootout win over AC Milan in the International Champions Cup on Saturday:
Pogba was not involved in the match in Cardiff after he suffered a back spasm on Tuesday.
However, Simon Jones and Chris Wheeler of the Daily Mail reported the midfielder took the club by surprise by not arriving for the team's flight to the Welsh capital on Friday, having been named in the travelling squad.
His absence was said to be part of an attempt to "force his way out" of the club in order to join Real Madrid.
Per Samuel Luckhurst of the Manchester Evening News, Solskjaer said he was not surprised by Pogba's absence:
"No, I wasn't expecting him. I spoke to him after training and he didn't feel right. And [press officer] Karen [Shotbolt] was busy talking to the press doing different things! So she takes the blame!
"He'll probably be back early on next week training, yeah. It's not an injury, it's just some pain. He's not injured but I wasn't going to risk anything this weekend. He should be okay for Chelsea."
The Frenchman contributed 16 goals and 11 assists in all competitions last season.
Although he has struggled for consistency at Old Trafford—much of his best form in the last campaign came in Solskjaer's first two months in charge—he's United's most creative player.
What's more, the Red Devils are yet to add to their midfield options ahead of Thursday's transfer deadline, but they have lost Ander Herrera.
As JOE's Nooruddean Choudry noted, the club are already short in that department even if Pogba stays:
Although United can continue to sell players until September 2, there is little time left for United to bring in a replacement for Pogba, as football writer Tom McDermott observed:
Tom McDermott @MrTomMcDermott
While I’m not a huge fan of Pogba, you see how desperate the #MUFC midfield looks without him. By selling him earlier in the window (like #CFC did with Hazard), United could have secured one/two replacements. That might be wishful thinking but this pantomime must end now.
Barring one or two top-class midfield arrivals in the coming days, United cannot afford to lose Pogba this summer.
As such, Solskjaer's comments are a positive sign for the Manchester outfit.